The solution of the system of differential equations dr = x+2y dt dy = 4x + 3y dt %3D Ce5t 2 - Czet , y = Cest + czet Or = Gest + c2et , y = Cet + C2et Cie5t + c2et , y = Cet + C2et Ciest Cze-t y = Cest C2e t Oa = cet C2e t ,y = C1e + c2et -

Q: Find a second linearly independent solution and write down the general solution: x²y" - 5xy' +9y =…

A: To find a second linear independent solution of the given problem where one solution is given.…

Q: dy = 2y and the solution to this equation includes the point (-1, 1), then y = dx 5. , Given (A) e²r…

A: Given : dy/dx= 2y includes point (-1, 1)

Q: Use the characteristics method to determine the solution for the equation d2y/dt2 + dy/dt +3y = 0.

A: Dear student we are write the ordinary differential equation so  we use the characteristic equation…

Q: In this equation, y=15x. What is the constant of proportionality?

A: Constant of proportionality is K then y/x = k is relation y = 15x y/x = 15 so that k = 15 i.e.…

Q: Solve the system dx dt with the initial value -4 [3] -3 x(0) = -11 9 [2:]- -6 4 x(t) = X

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Q: Solve the system d = dt with a1 (0) = 1 and æ2(0) = -1. %3D

A: The given system of differential equation: x1'x2'=   0-1-1   0 x1x2+t0  ;        x1(0)x2(0)=1-1

Q: general equation of (z-t)dz=(z+t)dt

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Q: find dy/dt.

A:

Q: Solve the system -8 6 dx dt -4 2 with the initial value 14 x(0) = x(t) =

A: Let's find.

Q: d²x_dx Verify that x = C,e¬t + C2e2t is a solution to dt2 2х — 0. - dt

A: To verify the given statement.

Q: The system dx/dt = x + y, dy/dt = x + 2y + 1 has a constant solution. true or false?

A: dx/dt = x + y,dy/dt = x + 2y + 1

Q: How do you integrate this: ∫(50+2t)3(10) dt + c c = is just an arbitrary constant

A: Indefinite Integration

Q: (1) Show that the system x=-2 cos x - cos y y=-2 cos y - cos x is reversible but not conservative.…

A: To show that the system is reversible but not conservative.And to plot the phase portrait

Q: du Solve the equation "u(0, y) = 8e» = 4. by the method of separation of variables.

A:

Q: Jse variation of parameters to find a solution o the given system: dx/dt%3D2Y+2…

A: Given system isdxdt = 2y+2 ; dydt = -x+3y+e-3t ; can be reduced asx'y' = 02-13xy+2e-3tis of the form…

Q: Find the stability of the system which has the following differential equation: y ̈+3 y ̇+2y=0 ,…

A: To find the stability of the system which has the following differential equation

Q: Q4/ In a mass-spring-damper system, the acceleration x₁ (m/s²), velocity x₂ (m/s) and displacement…

A: We are to solve for x_1 , x_2, x_3

Q: What is general solution of v = ds/dt if v = 2/t^3/2? a.-4/t^1/2 = s^2 + c b.-4/t^1/2 = s + c^2…

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Q: CALCULATE THE FOLLOWING USING MINOR COFACTOR AND COFACTOR EXPANSION 3 -8 2 A= 2 -6 3 4 4 2

A: A system of m×n numbers arranged in the form of a rectangular array having m rows and n columns is…

Q: plot a phase diagram of the following system x'=2y y'=-x-y

A: We have to plot a phase diagram of the given system  x'=2yy'=-x-y

Q: equations: dx/dt=-x+2y, dy/dt=2x+2y+e^(2t). Initial conditions are given by x(0)=0; y(0)=-34

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Q: The function u depends on two independent variables: u= u(x, t). Find the general solution of the…

A: Given: The function u depends on two independent variables: u=u(x,t). PDE: ∂2u∂t2+∂u∂t+u=2t-x. To…

Q: 12vt dt (1+t3/2)2

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Q: Find dX/dt of Matrix:

A:

Q: Find the solution of the partial differential equation- = 3 dt? by variable separable method

A: given partial differential equation  ∂2z∂x2=3∂2z∂t2 to find -solution of the partial differential…

Q: Why does dA/dt = 0?

A: Since area is constant therefore dA/dt=0

Q: True or False The system dx/dt = 2y dy/dt = sin(xy) has only one equilibrium point.

A: We need to equate both the derivative to 0, to calculate the equilibrium points.

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? (A…

A:

Q: * =* (1 --) dx dt dy = y dt y - X 4 - taking (x, y) > 0. (a) Write an equation for the (non-zero)…

A: Given- Consider the system of equations  dxdt = x1 - x3 - ydydt = y1 - y4 - x taking x, y > 0 To…

Q: system

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Q: x = 2x - xy + (1/2)x²

A:

Q: Consider the non-linear differential equation * =- x+ y – 1 ў 3 2х + х3. Draw the nullclines and a…

A: Regression Analysis:              Regression analysis helps to estimate the changes when…

Q: x' = Ax where A = 3 2 -2

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Q: t2+1 = 0 dv Vt- dt V+1

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Q: dy dt = = -2y + 8(t-3) + 2H(t-4), y(0) = 1.

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Q: DEGREE

A: We have to determine the order, degree and linearity of the given differential equations according…

Q: dy = 3x – Y dt dx 4x + 2y, dt (i) Show that x(t) = 10e5t –- e-2t and y(t) = 5e5t + 3e2t form a…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.